One of the most well-known and quite general methods is the "double-sum method", first proposed by Pickands [1]} and extended by Piterbarg [2]}, [3]}. The main idea of this method is to use the inclusion-exclusion principle and the Bonferroni inequality after dividing the parameter set into suitable smaller subsets. It was first proposed in dimension 1 : \(n=1\)  (in this case we use the classical terminology of "random processes" instead of "random field"). More precisely, for some particular processes, i.e., the "\(\alpha \)  processes", Pickands proposed an equivalent for the tail of the maximum. However, the result depends on some unknown constants,referred to as Pickands' constants and just gives an equivalent.
